Related papers: The hypersecant Jacobian approximation for quasi-N…
Quasi-Newton methods are well known techniques for large-scale numerical optimization. They use an approximation of the Hessian in optimization problems or the Jacobian in system of nonlinear equations. In the Interior Point context,…
We propose a new stochastic proximal quasi-Newton method for minimizing the sum of two convex functions in the particular context that one of the functions is the average of a large number of smooth functions and the other one is nonsmooth.…
Unique existence of analytically strong solutions to stochastic partial differential equations (SPDE) with drift given by the subdifferential of a quasi-convex function and with general multiplicative noise is proven. The proof applies a…
We investigate the computation of stable fracture paths in brittle thin films using one-dimensional damage models with an elastic foundation. The underlying variational formulation is non-convex, making the evolution path sensitive to…
Wereportonanewmultiscalemethodapproachforthestudyofsystemswith wide separation of short-range forces acting on short time scales and long-range forces acting on much slower scales. We consider the case of the Poisson-Boltzmann equation that…
We developed a weak-linked Josephson junction time-domain simulation tool based on the Bardeen-Cooper-Schrieffer (BCS) theory to account for the electrodynamics of Cooper pairs and quasiparticles in the presence of thermal noise. The model,…
Newton's method is an ubiquitous tool to solve equations, both in the archimedean and non-archimedean settings -- for which it does not really differ. Broyden was the instigator of what is called "quasi-Newton methods". These methods use an…
We introduce a new framework for analyzing (Quasi-}Newton type methods applied to non-smooth optimization problems. The source of randomness comes from the evaluation of the (approximation) of the Hessian. We derive, using a variant of…
Simulating compositional multiphase flow in porous media is a challenging task, especially when phase transition is taken into account. The main problem with phase transition stems from the inconsistency of the primary variables such as…
It has recently been shown that many of the existing quasi-Newton algorithms can be formulated as learning algorithms, capable of learning local models of the cost functions. Importantly, this understanding allows us to safely start…
Many problems give rise to polynomial systems. These systems often have several parameters and we are interested to study how the solutions vary when we change the values for the parameters. Using predictor-corrector methods we track the…
We present a quasi-Newton method for unconstrained stochastic optimization. Most existing literature on this topic assumes a setting of stochastic optimization in which a finite sum of component functions is a reasonable approximation of an…
The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…
The solution $\vartheta =(\vartheta_{t})_{t\geq 0}$ of a class of linear stochastic partial differential equations is approximated using Clark's robust representation approach (\cite{c}, \cite{cc}). The ensuing approximations are shown to…
We present an efficient algorithm for least-squares constrained nuclear norm minimization, a computationally challenging problem with broad applications. Our approach combines a level set method with secant iterations and a proximal…
The Quasi-Steady State Approximation (QSSA) can be an effective tool for reducing the size and stiffness of chemical mechanisms for implementation in computational reacting flow solvers. However, for many applications, stiffness remains,…
Quasi-Newton algorithms are among the most popular iterative methods for solving unconstrained minimization problems, largely due to their favorable superlinear convergence property. However, existing results for these algorithms are…
We present a new theoretical analysis of local superlinear convergence of classical quasi-Newton methods from the convex Broyden class. As a result, we obtain a significant improvement in the currently known estimates of the convergence…
This paper primarily presents numerical results for the Anderson accelerated Newton method on a set of benchmark problems. The results demonstrate superlinear convergence to solutions of both degenerate and nondegenerate problems. The…
We introduce a new class of fractional backward orthogonal functions designed for the spectral approximation of weakly singular adjoint Volterra integral equations. These basis functions generate an approximation space that naturally…